A 19th-century building in NoHo will be damaged or destroyed if the city approves a proposal to construct a hotel next door, preservation advocates say.

The Merchant’s House Museum on East Fourth Street, between Lafayette Street and Bowery, is the city’s only family home from the 1800s to be preserved with landmark status for both the exterior and interior. But if plans for an 8-story hotel next door move forward, the construction will damage the 3.5-story house, the museum says.

The developer, Kalodop Park Corporation, submitted an application to the City Planning Commission to amend a zoning rule that would otherwise block construction. The building’s height and plans for a restaurant on the ground floor are contrary to zoning code.

The application is currently being reviewed by Community Board 2, which has two months to vote on it before it moves to the borough president, the planning commission and eventually City Council.

The museum has spent tens of thousands of dollars on engineering studies to assess how the building would be damaged if there is construction next door, Executive Director Margaret Halsey Gardiner said. It also knows from experience — demolitions on either side of the building, one in 1945 and the other in 1988, already caused damage, she said.

“There’s no protective measure that could be taken to protect the house,” Gardiner said.

The highest risk is structural damage or collapse. At the very least, construction next door will damage the original plasterwork inside the building, said Michael Devonshire, who is the director of conservation at the architecture firm Jan Hird Pokorny Associates and serves on the city’s Landmarks Preservation Commission.